Yield Effects in Single and Coupled Nonlinear Thermokinetic Reaction Systems

The influence of nonlinear dynamic effects on yield is considered for consecutive-parallel reaction schemes in a single phase CSTR. In the first part, the behavior of a single uncoupled reactor is investigated. Emphasis is on the reaction dynamics and the yield of the intermediate ethanal using continuation and optimization techniques. We characterize regions of periodic, complex periodic, and chaotic oscillations. The chaotic region is reached by type III intermittency. In all cases, the global optimum yield of the intermediate is a steady state, which is unstable or stable due to the location of the stability boundary. It is found that autonomous periodic operation is only locally better than steady state operation. In the second part, different types of mass and energy coupling between two reactors are studied. The results obtained for a simple consecutive parallel reaction scheme are validated by a more detailed model of the ethanol oxidation by hydrogen peroxide under iron(III) catalysis, which can be described by an extended consecutive-parallel reaction scheme. Analogies are found with respect to the dynamics and the yield of the intermediate.

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Steady State and Dynamic Analyses of Supercritical CO2 Natural Circulation Loop

Volume 2: Thermal Hydraulics ◽

10.1115/icone14-89103 ◽

2006 ◽

Cited By ~ 2

Author(s):

Prashant Jain ◽

Rizwan Uddin

Keyword(s):

Steady State ◽

Natural Circulation ◽

Stability Boundary ◽

Operating Conditions ◽

Circulation Loop ◽

Steady State Flow ◽

Natural Circulation Loop ◽

Dynamic Analyses ◽

The Stability ◽

Flow Power

Numerical studies have been carried out to investigate supercritical flow instabilities in a CO2 natural circulation loop. For the steady state and dynamic analyses of the loop under supercritical conditions, a single-channel, one-dimensional model is developed. In this model, equations for the conservation of mass, momentum and energy are discretized using an implicit finite difference scheme. A computer code called FIASCO (Flow Instability Analysis under SuperCritical Operating conditions) is developed in FORTRAN90 to simulate the dynamics of natural circulation loops with supercritical fluid. Results obtained for the stability boundary substantially deviate from the results reported by previous investigators, and thus contradict some of the reported findings. The disagreement in results is most likely due to the undesirable dissipative and dispersive effects produced from the large time steps used in previous studies, thereby leading to a larger stable region than those found using smaller time step. Results presented here suggest that the stability boundary of a natural circulation loop with supercritical fluid, is not confined to the near-peak region of the (steady state) flow-power curve. Additional and more extensive experimental data are needed to resolve the differences between results obtained here and those reported earlier. However, results obtained for the range of parameter values used in this investigation always predict the stability threshold to be in the positive slope region of the (steady state) flow-power curve. Parametric studies for different operating conditions reveal the similarity of stability characteristics under supercritical conditions with those in two-phase flows.

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Travelling Wave and Turing Patterns in Subdiffusive Autocatalytic Systems

10.21203/rs.3.rs-896566/v1 ◽

2021 ◽

Author(s):

Uttam Kumar ◽

Pushpavanam Subramanian

Keyword(s):

Steady State ◽

Stability Boundary ◽

Mean Square Displacement ◽

Travelling Wave ◽

Turing Patterns ◽

Logistic Growth ◽

Stable Steady State ◽

Phase Plane Analysis ◽

Plane Analysis ◽

The Stability

Abstract In this work, we analyse autocatalytic reactions in complex and disordered media which are governed by subdiffusion. The mean square displacement of molecules here scale as tγ where 0<γ<1. These systems are governed by fractional partial differential equations. Two systems are analysed i) in the first a logistic growth expression is used to represent the growth kinetics of bacteria. Here the system dynamics is governed by a single variable. ii) the second system is a two variable cubic autocatalytic system in a porous media. Here each reactant is involved in the autocatalytic generation of the other. These systems have multiple steady states. They exhibit traveling waves moving from an unstable steady state to a stable steady state. The minimum wave velocity has been obtained from phase plane analysis analytically for the first system. In addition, the two variable system also shows Turing patterns in selected regions of parameter space. The stability boundary for Turing patterns for subdiffusive system is found to be the same as that for regular diffusive systems obtained by Seshai et al. [1]. System behaviour as predicted by the stability analysis is verified using a robust implicit numerical method based on L1 scheme.

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State estimation for a biological phosphorus removal process using an asymptotic observer

Water Science & Technology ◽

10.2166/wst.2001.0684 ◽

2001 ◽

Vol 43 (11) ◽

pp. 205-213 ◽

Cited By ~ 1

Author(s):

A. Larose ◽

S. B. Jørgensen

Keyword(s):

Steady State ◽

State Estimation ◽

Phosphorus Removal ◽

Reaction Scheme ◽

Biological Phosphorus Removal ◽

Removal Process ◽

Steady State Operation ◽

Asymptotic Observer ◽

Biological Phosphorus ◽

High Condition

This study investigated the use of an asymptotic observer for state estimation in a continuous biological phosphorus removal process. The estimated states are the concentration of heterotrophic, autotrophic and phosphorus accumulating organisms, polyphosphate, glycogen and PHA. The reaction scheme describing the process was simplified from a combined ASM1-Delft model. Three examples were investigated: operation at steady state, operation at steady state with a random white-noise in the measurements and operation with a ramp disturbance. In each case, the estimation was quite accurate even if the convergence, driven by the dilution rate, was slow (from 15 to 60 days). The propagation of the measurement noise and a bias in the estimation of glycogen and PHA could be the result of the high condition number of one of the matrices used in the algorithm of the asymptotic observer for the aerated tanks.

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A Method for Evaluating the Aerodynamic Stability of Multi-Stage Axial-Flow Compressors

Volume 7: Turbomachinery, Parts A and B ◽

10.1115/gt2009-60220 ◽

2009 ◽

Author(s):

Tsuguji Nakano ◽

Andy Breeze-Stringfellow

Keyword(s):

Steady State ◽

Flow Field ◽

Stability Boundary ◽

Axial Flow ◽

Pressure Rise ◽

State Density ◽

Constant Density ◽

Multi Stage ◽

The Stability ◽

Axial Flow Compressors

A new simple engineering parameter to evaluate the stability of multi-stage axial compressors has been derived. It is based on the stability analysis for a small circumferential disturbance imposed on the steady state flow field. The analytical model assumes that the flow field is two dimensional and incompressible in the ducts between blade rows although the steady state density is permitted to change across the blade rows. The resulting stall parameter contains terms that relate to the slope of the pressure rise characteristic of the blade rows and the inertia effects of the fluid in the blade rows and ducts. The parameter leads to the classical stability criteria based on the slope of the overall total to static pressure rise coefficient in the limit where constant density and constant blade rotational speed are assumed across the compressor. The proposed stall parameter has been calculated for three different multi-stage axial flow compressors and the results indicate that the parameter has a strong correlation with the measured stability of the compressors. The good correlation with the test data demonstrates that the newly derived stall parameter captures much of the fundamental physics of instability inception in multi-stage compressors, and that it can be a good guideline for designers and engineers needing to evaluate the stability boundary of multi-stage machines.

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Dynamic Energy Efficient Control of Induction Machines Using Anticipative Flux Templates

Applied Sciences ◽

10.3390/app11062878 ◽

2021 ◽

Vol 11 (6) ◽

pp. 2878

Author(s):

Antony Dominic ◽

Gernot Schullerus ◽

Martin Winter

Keyword(s):

Energy Efficiency ◽

Steady State ◽

Real World ◽

Optimal Solution ◽

Induction Machines ◽

Optimization Techniques ◽

Efficiency Optimization ◽

Dynamic Operation ◽

Energy Efficiency Improvement ◽

Steady State Operation

Energy efficiency optimization techniques for steady state operation of induction machines are the state-of-the-art, and many methods have already been developed. However, many real-world industrial and electric vehicle applications cannot be considered to be in steady state operation. The focus of this contribution is on the efficiency optimization of induction machines in dynamic operation. Online dynamic operation is challenging due to the computational complexity and the required low sample times in an inverter. An offline optimization is therefore conducted to gain knowledge. Based on this offline optimal solution, a simple and easy to implement template based solution is developed. This approach aims at replicating the solution found by the offline optimization by resembling the shape and anticipative characteristics of the optimal flux trajectory. The energy efficiency improvement of the template based solution is verified by simulations and measurements on a test bench and using a real-world drive cycle scenario. For comparison, a model predictive numerical online optimization is investigated too.

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The Stability of Steady-State Depth Distributions of Marine Phytoplankton

The American Naturalist ◽

10.1086/282943 ◽

1974 ◽

Vol 108 (963) ◽

pp. 679-687 ◽

Cited By ~ 9

Author(s):

W. O. Criminale, ◽

D. F. Winter

Keyword(s):

Steady State ◽

Marine Phytoplankton ◽

The Stability ◽

Depth Distributions

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Steady-state $$\dot{V}{\text{O}}_{2}$$ above MLSS: evidence that critical speed better represents maximal metabolic steady state in well-trained runners

European Journal of Applied Physiology ◽

10.1007/s00421-021-04780-8 ◽

2021 ◽

Author(s):

Rebekah J. Nixon ◽

Sascha H. Kranen ◽

Anni Vanhatalo ◽

Andrew M. Jones

Keyword(s):

Steady State ◽

Critical Speed ◽

Lactate Concentration ◽

Practical Interest ◽

Blood Lactate Concentration ◽

Distance Runners ◽

Severe Intensity ◽

The Stability ◽

Trained Runners ◽

Over Time

AbstractThe metabolic boundary separating the heavy-intensity and severe-intensity exercise domains is of scientific and practical interest but there is controversy concerning whether the maximal lactate steady state (MLSS) or critical power (synonymous with critical speed, CS) better represents this boundary. We measured the running speeds at MLSS and CS and investigated their ability to discriminate speeds at which $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 was stable over time from speeds at which a steady-state $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 could not be established. Ten well-trained male distance runners completed 9–12 constant-speed treadmill tests, including 3–5 runs of up to 30-min duration for the assessment of MLSS and at least 4 runs performed to the limit of tolerance for assessment of CS. The running speeds at CS and MLSS were significantly different (16.4 ± 1.3 vs. 15.2 ± 0.9 km/h, respectively; P < 0.001). Blood lactate concentration was higher and increased with time at a speed 0.5 km/h higher than MLSS compared to MLSS (P < 0.01); however, pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 did not change significantly between 10 and 30 min at either MLSS or MLSS + 0.5 km/h. In contrast, $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 increased significantly over time and reached $$\dot{V}{\text{O}}_{2\,\,\max }$$ V ˙ O 2 max at end-exercise at a speed ~ 0.4 km/h above CS (P < 0.05) but remained stable at a speed ~ 0.5 km/h below CS. The stability of $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 at a speed exceeding MLSS suggests that MLSS underestimates the maximal metabolic steady state. These results indicate that CS more closely represents the maximal metabolic steady state when the latter is appropriately defined according to the ability to stabilise pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 .

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